Author
Erbay, Saadet, Erkip, A., Kuruk, G.
Publication Date
2022-09
Publication Place
-
Springer
Subject
Asymptotic expansion, Camassa-Holm equation, Double dispersion equation, Long time existence, Rigorous justification
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0026-9255
Record ID
26a24983-9bf7-4735-a0d6-95417451266e
Library Location
Natural and Mathematical Sciences
Date
2022-09
Sample Text
In the present paper we prove the validity of the Camassa-Holm equation as a long wave limit to the double dispersion equation which describes the propagation of bidirectional weakly nonlinear and dispersive waves in an infinite elastic medium. First we show formally that the right-going wave solutions of the double dispersion equation can be approximated by the solutions of the Camassa-Holm equation in the long wave limit. Then we rigorously prove that the solutions of the double dispersion and the Camassa-Holm equations remain close over a long time interval, determined by two small parameters measuring the effects of nonlinearity and dispersion.
DOI
10.1007/s00605-022-01740-y
Cilt
199
